A296993 Numbers k such that k^3 divides tau(k), where tau(k) = A000594(k) is Ramanujan's tau function.

1, 2, 4, 6, 8, 16, 24, 32, 64, 96, 128, 256, 288, 384, 512, 1024, 1536, 2048, 4096, 6144, 8192, 16384, 18432, 24576, 32768, 65536, 98304, 131072, 172032, 262144, 276480, 393216, 524288, 1048576, 1179648, 1572864, 1935360, 2097152, 2621440, 3538944, 4194304

Offset

1,2

Comments

2^k is a term for k >= 0.

Links

Table of n, a(n) for n=1..41.

Eric Weisstein's World of Mathematics, Tau Function.

Prog

(Python)
from itertools import count, islice
from sympy import divisor_sigma
def A296993_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: not -24*((m:=n+1>>1)**2*(0 if n&1 else (m*(35*m - 52*n) + 18*n**2)*divisor_sigma(m)**2)+sum((i*(i*(i*(70*i - 140*n) + 90*n**2)))*divisor_sigma(i)*divisor_sigma(n-i) for i in range(1, m))) % n**3, count(max(startvalue, 1)))
A296993_list = list(islice(A296993_gen(), 10)) # Chai Wah Wu, Nov 08 2022

Crossrefs

Cf. A000594, A063938, A296991, A296992.

Sequence in context: A064408 A316225 A100685 * A068799 A317306 A317087

Adjacent sequences: A296990 A296991 A296992 * A296994 A296995 A296996

Keyword

nonn

Author

Seiichi Manyama, Dec 22 2017

Status

approved